INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1152 Minimal number of generators: 193 Number of equivalence classes of cusps: 72 Genus: 61 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -10/1 -8/1 -7/1 -6/1 -16/3 -21/4 -4/1 -7/2 -8/3 -21/8 -7/3 -2/1 -7/4 -12/7 -7/5 -4/3 -21/16 -7/6 0/1 1/1 7/6 28/23 14/11 21/16 4/3 7/5 3/2 14/9 84/53 28/17 12/7 7/4 2/1 28/13 7/3 196/83 112/47 5/2 28/11 70/27 21/8 8/3 14/5 3/1 42/13 7/2 112/31 56/15 4/1 13/3 84/19 9/2 14/3 19/4 29/6 5/1 31/6 21/4 16/3 11/2 28/5 23/4 6/1 13/2 7/1 15/2 8/1 17/2 9/1 10/1 11/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -10/1 -1/4 -9/1 1/8 -8/1 1/2 1/0 -15/2 0/1 1/0 -7/1 1/0 -6/1 1/0 -23/4 -1/2 -1/3 -17/3 -1/4 -28/5 0/1 -11/2 0/1 1/2 -16/3 1/2 1/0 -21/4 1/0 -26/5 1/0 -5/1 1/0 -19/4 0/1 1/0 -14/3 1/0 -9/2 -1/1 1/0 -22/5 -3/4 -13/3 1/0 -30/7 -3/4 -47/11 -11/16 -17/4 -1/1 -1/2 -4/1 -1/2 1/0 -19/5 -5/12 -34/9 -1/4 -15/4 -1/4 0/1 -26/7 1/0 -11/3 1/0 -7/2 -1/2 -17/5 -3/8 -27/8 -3/8 -1/3 -10/3 -1/4 -13/4 -1/3 -1/4 -42/13 -1/4 -29/9 -1/4 -16/5 -1/4 -1/6 -3/1 1/0 -20/7 -3/4 -1/2 -37/13 -13/20 -17/6 -3/5 -1/2 -14/5 -1/2 -11/4 -1/2 -2/5 -19/7 -7/20 -46/17 -5/16 -27/10 -1/3 -1/4 -8/3 -1/2 -1/4 -29/11 1/0 -21/8 -1/2 -55/21 -3/8 -89/34 -1/2 -3/7 -34/13 -3/8 -13/5 -1/4 -31/12 0/1 1/0 -18/7 -1/4 -41/16 -1/4 0/1 -64/25 -1/2 -1/4 -23/9 -1/4 -28/11 0/1 -5/2 -1/2 0/1 -17/7 -1/4 -29/12 -1/3 -1/4 -12/5 -1/2 -1/4 -31/13 -1/8 -50/21 1/0 -19/8 -1/4 0/1 -26/11 1/0 -7/3 -1/2 -30/13 -3/8 -83/36 -1/3 -1/4 -53/23 -1/4 -23/10 -1/2 -1/3 -39/17 -3/8 -55/24 -2/5 -3/8 -16/7 -1/2 -3/8 -41/18 -3/8 -4/11 -66/29 -3/8 -25/11 -7/20 -84/37 -1/3 -59/26 -1/3 -9/28 -34/15 -1/4 -9/4 -3/8 -1/3 -20/9 -3/10 -1/4 -11/5 -1/4 -13/6 -3/8 -1/3 -28/13 -1/3 -15/7 -5/16 -2/1 -1/4 -11/6 -1/2 0/1 -9/5 -5/16 -7/4 -1/4 -19/11 -11/48 -31/18 -2/9 -7/32 -43/25 -1/4 -55/32 -1/4 -2/9 -12/7 -1/4 -3/14 -41/24 -1/4 0/1 -70/41 -1/4 -29/17 -1/4 -17/10 -3/14 -1/5 -22/13 -1/4 -27/16 -1/4 -1/5 -5/3 -1/4 -28/17 -1/5 -23/14 -1/5 -1/6 -18/11 -1/4 -13/8 -1/4 -1/5 -34/21 -1/4 -21/13 -1/4 -71/44 -1/4 -2/9 -50/31 -1/4 -29/18 -1/4 -1/5 -8/5 -1/4 -1/6 -27/17 -1/8 -19/12 0/1 1/0 -30/19 -1/4 -11/7 -1/4 -36/23 -3/10 -1/4 -61/39 -1/4 -86/55 -1/4 -25/16 -2/7 -1/4 -14/9 -1/4 -3/2 -1/4 -1/5 -22/15 -7/36 -19/13 -13/68 -54/37 -3/16 -35/24 -3/16 -16/11 -3/16 -1/6 -29/20 -1/5 -3/16 -42/29 -3/16 -55/38 -3/16 -2/11 -13/9 -3/16 -36/25 -3/16 -1/6 -59/41 -1/4 -23/16 -1/5 -1/6 -10/7 -3/16 -47/33 -27/148 -84/59 -2/11 -37/26 -2/11 -21/116 -27/19 -5/28 -17/12 -3/17 -1/6 -24/17 -7/40 -1/6 -7/5 -1/6 -32/23 -1/6 -5/32 -57/41 -7/44 -196/141 -3/19 -139/100 -3/19 -17/108 -82/59 -5/32 -25/18 -5/32 -2/13 -18/13 -3/20 -65/47 -15/104 -112/81 -1/7 -47/34 -1/7 -9/64 -29/21 -1/8 -40/29 -1/6 -1/8 -11/8 -1/6 0/1 -26/19 -1/8 -41/30 -1/12 0/1 -56/41 0/1 -15/11 -1/4 -19/14 -1/4 0/1 -23/17 -1/4 -27/20 -1/4 -1/5 -4/3 -1/4 -1/6 -29/22 -1/4 -1/5 -25/19 -1/4 -21/16 -1/6 -59/45 -3/20 -38/29 -1/8 -55/42 -1/4 0/1 -17/13 -1/4 -13/10 -1/5 -3/16 -22/17 -3/16 -53/41 -19/104 -84/65 -2/11 -31/24 -2/11 -13/72 -9/7 -7/40 -32/25 -13/76 -1/6 -55/43 -15/88 -23/18 -9/53 -1/6 -14/11 -1/6 -5/4 -1/6 -2/13 -11/9 -3/20 -28/23 -1/7 -17/14 -1/7 -3/22 -6/5 -1/8 -19/16 -1/4 0/1 -13/11 -1/4 -7/6 -1/6 -15/13 -3/20 -8/7 -1/6 -3/20 -9/8 -7/48 -1/7 -1/1 -1/8 0/1 0/1 1/1 1/8 8/7 3/20 1/6 7/6 1/6 20/17 1/6 1/4 13/11 1/4 6/5 1/8 17/14 3/22 1/7 28/23 1/7 11/9 3/20 5/4 2/13 1/6 14/11 1/6 23/18 1/6 9/53 9/7 7/40 22/17 3/16 13/10 3/16 1/5 17/13 1/4 38/29 1/8 21/16 1/6 25/19 1/4 4/3 1/6 1/4 19/14 0/1 1/4 34/25 1/8 15/11 1/4 11/8 0/1 1/6 29/21 1/8 47/34 9/64 1/7 18/13 3/20 25/18 2/13 5/32 7/5 1/6 31/22 4/23 7/40 86/61 7/40 55/39 5/28 24/17 1/6 7/40 17/12 1/6 3/17 27/19 5/28 10/7 3/16 23/16 1/6 1/5 36/25 1/6 3/16 13/9 3/16 16/11 1/6 3/16 19/13 13/68 3/2 1/5 1/4 14/9 1/4 25/16 1/4 2/7 11/7 1/4 30/19 1/4 19/12 0/1 1/0 84/53 0/1 65/41 1/24 46/29 1/12 27/17 1/8 8/5 1/6 1/4 29/18 1/5 1/4 50/31 1/4 21/13 1/4 13/8 1/5 1/4 18/11 1/4 23/14 1/6 1/5 28/17 1/5 5/3 1/4 27/16 1/5 1/4 22/13 1/4 17/10 1/5 3/14 29/17 1/4 70/41 1/4 41/24 0/1 1/4 12/7 3/14 1/4 7/4 1/4 16/9 1/4 5/18 25/14 9/32 2/7 34/19 7/24 9/5 5/16 11/6 0/1 1/2 13/7 1/0 2/1 1/4 15/7 5/16 28/13 1/3 13/6 1/3 3/8 11/5 1/4 31/14 1/4 2/7 51/23 1/4 20/9 1/4 3/10 29/13 5/16 9/4 1/3 3/8 25/11 7/20 41/18 4/11 3/8 16/7 3/8 1/2 55/24 3/8 2/5 39/17 3/8 23/10 1/3 1/2 7/3 1/2 33/14 1/2 1/1 59/25 3/4 85/36 3/4 1/1 196/83 1/1 111/47 5/4 26/11 1/0 19/8 0/1 1/4 50/21 1/0 81/34 -1/8 0/1 112/47 0/1 31/13 1/8 12/5 1/4 1/2 41/17 1/4 70/29 1/4 29/12 1/4 1/3 17/7 1/4 5/2 0/1 1/2 28/11 0/1 23/9 1/4 41/16 0/1 1/4 59/23 3/8 77/30 1/2 18/7 1/4 31/12 0/1 1/0 44/17 1/4 1/2 57/22 0/1 1/4 70/27 1/4 13/5 1/4 34/13 3/8 21/8 1/2 50/19 1/0 29/11 1/0 8/3 1/4 1/2 27/10 1/4 1/3 19/7 7/20 11/4 2/5 1/2 14/5 1/2 17/6 1/2 3/5 20/7 1/2 3/4 23/8 1/2 1/1 3/1 1/0 16/5 1/6 1/4 29/9 1/4 42/13 1/4 13/4 1/4 1/3 10/3 1/4 7/2 1/2 18/5 3/4 65/18 15/16 1/1 112/31 1/1 47/13 9/8 29/8 1/1 1/0 11/3 1/0 26/7 1/0 41/11 -1/4 56/15 0/1 15/4 0/1 1/4 34/9 1/4 53/14 1/3 7/20 19/5 5/12 23/6 1/2 3/5 27/7 3/4 4/1 1/2 1/0 17/4 1/2 1/1 47/11 11/16 30/7 3/4 13/3 1/0 22/5 3/4 53/12 11/12 1/1 84/19 1/1 31/7 5/4 9/2 1/1 1/0 14/3 1/0 19/4 0/1 1/0 24/5 1/2 1/0 53/11 1/0 29/6 1/1 1/0 5/1 1/0 31/6 0/1 1/0 26/5 1/0 21/4 1/0 58/11 1/0 37/7 -7/4 16/3 -1/2 1/0 27/5 1/0 11/2 -1/2 0/1 28/5 0/1 17/3 1/4 23/4 1/3 1/2 29/5 1/0 6/1 1/0 13/2 1/1 1/0 7/1 1/0 22/3 1/0 15/2 0/1 1/0 23/3 1/0 8/1 -1/2 1/0 17/2 -1/2 -1/3 9/1 -1/8 10/1 1/4 11/1 1/0 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(55,588,-42,-449) (-10/1,1/0) -> (-38/29,-55/42) Hyperbolic Matrix(111,1064,70,671) (-10/1,-9/1) -> (65/41,46/29) Hyperbolic Matrix(57,476,-20,-167) (-9/1,-8/1) -> (-20/7,-37/13) Hyperbolic Matrix(169,1288,-66,-503) (-8/1,-15/2) -> (-41/16,-64/25) Hyperbolic Matrix(113,812,-70,-503) (-15/2,-7/1) -> (-21/13,-71/44) Hyperbolic Matrix(55,364,-34,-225) (-7/1,-6/1) -> (-34/21,-21/13) Hyperbolic Matrix(225,1316,-86,-503) (-6/1,-23/4) -> (-89/34,-34/13) Hyperbolic Matrix(225,1288,98,561) (-23/4,-17/3) -> (39/17,23/10) Hyperbolic Matrix(169,952,30,169) (-17/3,-28/5) -> (28/5,17/3) Hyperbolic Matrix(111,616,20,111) (-28/5,-11/2) -> (11/2,28/5) Hyperbolic Matrix(113,616,-82,-447) (-11/2,-16/3) -> (-40/29,-11/8) Hyperbolic Matrix(169,896,-116,-615) (-16/3,-21/4) -> (-35/24,-16/11) Hyperbolic Matrix(391,2044,-268,-1401) (-21/4,-26/5) -> (-54/37,-35/24) Hyperbolic Matrix(391,2016,-250,-1289) (-26/5,-5/1) -> (-61/39,-86/55) Hyperbolic Matrix(111,532,-82,-393) (-5/1,-19/4) -> (-19/14,-23/17) Hyperbolic Matrix(113,532,24,113) (-19/4,-14/3) -> (14/3,19/4) Hyperbolic Matrix(55,252,12,55) (-14/3,-9/2) -> (9/2,14/3) Hyperbolic Matrix(113,504,-50,-223) (-9/2,-22/5) -> (-34/15,-9/4) Hyperbolic Matrix(167,728,64,279) (-22/5,-13/3) -> (13/5,34/13) Hyperbolic Matrix(111,476,52,223) (-13/3,-30/7) -> (2/1,15/7) Hyperbolic Matrix(727,3108,-498,-2129) (-30/7,-47/11) -> (-19/13,-54/37) Hyperbolic Matrix(223,952,26,111) (-47/11,-17/4) -> (17/2,9/1) Hyperbolic Matrix(113,476,80,337) (-17/4,-4/1) -> (24/17,17/12) Hyperbolic Matrix(169,644,-132,-503) (-4/1,-19/5) -> (-9/7,-32/25) Hyperbolic Matrix(281,1064,-192,-727) (-19/5,-34/9) -> (-22/15,-19/13) Hyperbolic Matrix(839,3164,-520,-1961) (-34/9,-15/4) -> (-71/44,-50/31) Hyperbolic Matrix(391,1456,-286,-1065) (-15/4,-26/7) -> (-26/19,-41/30) Hyperbolic Matrix(167,616,106,391) (-26/7,-11/3) -> (11/7,30/19) Hyperbolic Matrix(55,196,-16,-57) (-11/3,-7/2) -> (-7/2,-17/5) Parabolic Matrix(281,952,116,393) (-17/5,-27/8) -> (29/12,17/7) Hyperbolic Matrix(449,1512,-166,-559) (-27/8,-10/3) -> (-46/17,-27/10) Hyperbolic Matrix(111,364,68,223) (-10/3,-13/4) -> (13/8,18/11) Hyperbolic Matrix(337,1092,104,337) (-13/4,-42/13) -> (42/13,13/4) Hyperbolic Matrix(1007,3248,590,1903) (-42/13,-29/9) -> (29/17,70/41) Hyperbolic Matrix(279,896,52,167) (-29/9,-16/5) -> (16/3,27/5) Hyperbolic Matrix(167,532,70,223) (-16/5,-3/1) -> (31/13,12/5) Hyperbolic Matrix(449,1288,-312,-895) (-3/1,-20/7) -> (-36/25,-59/41) Hyperbolic Matrix(503,1428,118,335) (-37/13,-17/6) -> (17/4,47/11) Hyperbolic Matrix(169,476,60,169) (-17/6,-14/5) -> (14/5,17/6) Hyperbolic Matrix(111,308,40,111) (-14/5,-11/4) -> (11/4,14/5) Hyperbolic Matrix(113,308,62,169) (-11/4,-19/7) -> (9/5,11/6) Hyperbolic Matrix(1231,3332,-890,-2409) (-19/7,-46/17) -> (-18/13,-65/47) Hyperbolic Matrix(167,448,104,279) (-27/10,-8/3) -> (8/5,29/18) Hyperbolic Matrix(169,448,106,281) (-8/3,-29/11) -> (27/17,8/5) Hyperbolic Matrix(671,1764,-256,-673) (-29/11,-21/8) -> (-21/8,-55/21) Parabolic Matrix(1401,3668,364,953) (-55/21,-89/34) -> (23/6,27/7) Hyperbolic Matrix(279,728,64,167) (-34/13,-13/5) -> (13/3,22/5) Hyperbolic Matrix(671,1736,-390,-1009) (-13/5,-31/12) -> (-31/18,-43/25) Hyperbolic Matrix(391,1008,282,727) (-31/12,-18/7) -> (18/13,25/18) Hyperbolic Matrix(1343,3444,-590,-1513) (-18/7,-41/16) -> (-41/18,-66/29) Hyperbolic Matrix(1455,3724,656,1679) (-64/25,-23/9) -> (51/23,20/9) Hyperbolic Matrix(505,1288,198,505) (-23/9,-28/11) -> (28/11,23/9) Hyperbolic Matrix(111,280,44,111) (-28/11,-5/2) -> (5/2,28/11) Hyperbolic Matrix(57,140,46,113) (-5/2,-17/7) -> (11/9,5/4) Hyperbolic Matrix(335,812,92,223) (-17/7,-29/12) -> (29/8,11/3) Hyperbolic Matrix(337,812,-232,-559) (-29/12,-12/5) -> (-16/11,-29/20) Hyperbolic Matrix(223,532,70,167) (-12/5,-31/13) -> (3/1,16/5) Hyperbolic Matrix(1399,3332,-1082,-2577) (-31/13,-50/21) -> (-22/17,-53/41) Hyperbolic Matrix(671,1596,494,1175) (-50/21,-19/8) -> (19/14,34/25) Hyperbolic Matrix(449,1064,284,673) (-19/8,-26/11) -> (30/19,19/12) Hyperbolic Matrix(167,392,-72,-169) (-26/11,-7/3) -> (-7/3,-30/13) Parabolic Matrix(4759,10976,-3424,-7897) (-30/13,-83/36) -> (-139/100,-82/59) Hyperbolic Matrix(2575,5936,534,1231) (-83/36,-53/23) -> (53/11,29/6) Hyperbolic Matrix(559,1288,194,447) (-53/23,-23/10) -> (23/8,3/1) Hyperbolic Matrix(561,1288,98,225) (-23/10,-39/17) -> (17/3,23/4) Hyperbolic Matrix(1343,3080,-1026,-2353) (-39/17,-55/24) -> (-55/42,-17/13) Hyperbolic Matrix(1455,3332,562,1287) (-55/24,-16/7) -> (44/17,57/22) Hyperbolic Matrix(503,1148,294,671) (-16/7,-41/18) -> (41/24,12/7) Hyperbolic Matrix(2129,4844,-1624,-3695) (-66/29,-25/11) -> (-59/45,-38/29) Hyperbolic Matrix(2071,4704,468,1063) (-25/11,-84/37) -> (84/19,31/7) Hyperbolic Matrix(4145,9408,938,2129) (-84/37,-59/26) -> (53/12,84/19) Hyperbolic Matrix(1679,3808,444,1007) (-59/26,-34/15) -> (34/9,53/14) Hyperbolic Matrix(113,252,-100,-223) (-9/4,-20/9) -> (-8/7,-9/8) Hyperbolic Matrix(279,616,-178,-393) (-20/9,-11/5) -> (-11/7,-36/23) Hyperbolic Matrix(167,364,128,279) (-11/5,-13/6) -> (13/10,17/13) Hyperbolic Matrix(337,728,156,337) (-13/6,-28/13) -> (28/13,13/6) Hyperbolic Matrix(391,840,182,391) (-28/13,-15/7) -> (15/7,28/13) Hyperbolic Matrix(223,476,52,111) (-15/7,-2/1) -> (30/7,13/3) Hyperbolic Matrix(167,308,-122,-225) (-2/1,-11/6) -> (-11/8,-26/19) Hyperbolic Matrix(169,308,62,113) (-11/6,-9/5) -> (19/7,11/4) Hyperbolic Matrix(111,196,-64,-113) (-9/5,-7/4) -> (-7/4,-19/11) Parabolic Matrix(503,868,-390,-673) (-19/11,-31/18) -> (-31/24,-9/7) Hyperbolic Matrix(1791,3080,-1238,-2129) (-43/25,-55/32) -> (-55/38,-13/9) Hyperbolic Matrix(897,1540,392,673) (-55/32,-12/7) -> (16/7,55/24) Hyperbolic Matrix(671,1148,294,503) (-12/7,-41/24) -> (41/18,16/7) Hyperbolic Matrix(3361,5740,1968,3361) (-41/24,-70/41) -> (70/41,41/24) Hyperbolic Matrix(1903,3248,590,1007) (-70/41,-29/17) -> (29/9,42/13) Hyperbolic Matrix(559,952,394,671) (-29/17,-17/10) -> (17/12,27/19) Hyperbolic Matrix(281,476,232,393) (-17/10,-22/13) -> (6/5,17/14) Hyperbolic Matrix(1177,1988,730,1233) (-22/13,-27/16) -> (29/18,50/31) Hyperbolic Matrix(449,756,-332,-559) (-27/16,-5/3) -> (-23/17,-27/20) Hyperbolic Matrix(169,280,102,169) (-5/3,-28/17) -> (28/17,5/3) Hyperbolic Matrix(783,1288,476,783) (-28/17,-23/14) -> (23/14,28/17) Hyperbolic Matrix(393,644,274,449) (-23/14,-18/11) -> (10/7,23/16) Hyperbolic Matrix(223,364,68,111) (-18/11,-13/8) -> (13/4,10/3) Hyperbolic Matrix(449,728,346,561) (-13/8,-34/21) -> (22/17,13/10) Hyperbolic Matrix(1233,1988,730,1177) (-50/31,-29/18) -> (27/16,22/13) Hyperbolic Matrix(279,448,104,167) (-29/18,-8/5) -> (8/3,27/10) Hyperbolic Matrix(281,448,106,169) (-8/5,-27/17) -> (29/11,8/3) Hyperbolic Matrix(953,1512,-670,-1063) (-27/17,-19/12) -> (-37/26,-27/19) Hyperbolic Matrix(673,1064,284,449) (-19/12,-30/19) -> (26/11,19/8) Hyperbolic Matrix(391,616,106,167) (-30/19,-11/7) -> (11/3,26/7) Hyperbolic Matrix(841,1316,108,169) (-36/23,-61/39) -> (23/3,8/1) Hyperbolic Matrix(3081,4816,2186,3417) (-86/55,-25/16) -> (31/22,86/61) Hyperbolic Matrix(449,700,288,449) (-25/16,-14/9) -> (14/9,25/16) Hyperbolic Matrix(55,84,36,55) (-14/9,-3/2) -> (3/2,14/9) Hyperbolic Matrix(839,1232,190,279) (-3/2,-22/15) -> (22/5,53/12) Hyperbolic Matrix(2241,3248,928,1345) (-29/20,-42/29) -> (70/29,29/12) Hyperbolic Matrix(4313,6244,1664,2409) (-42/29,-55/38) -> (57/22,70/27) Hyperbolic Matrix(505,728,428,617) (-13/9,-36/25) -> (20/17,13/11) Hyperbolic Matrix(2297,3304,974,1401) (-59/41,-23/16) -> (33/14,59/25) Hyperbolic Matrix(449,644,274,393) (-23/16,-10/7) -> (18/11,23/14) Hyperbolic Matrix(393,560,40,57) (-10/7,-47/33) -> (9/1,10/1) Hyperbolic Matrix(6607,9408,4168,5935) (-47/33,-84/59) -> (84/53,65/41) Hyperbolic Matrix(3305,4704,2086,2969) (-84/59,-37/26) -> (19/12,84/53) Hyperbolic Matrix(671,952,394,559) (-27/19,-17/12) -> (17/10,29/17) Hyperbolic Matrix(337,476,80,113) (-17/12,-24/17) -> (4/1,17/4) Hyperbolic Matrix(279,392,-200,-281) (-24/17,-7/5) -> (-7/5,-32/23) Parabolic Matrix(785,1092,202,281) (-32/23,-57/41) -> (27/7,4/1) Hyperbolic Matrix(23687,32928,10030,13943) (-57/41,-196/141) -> (196/83,111/47) Hyperbolic Matrix(31585,43904,13376,18593) (-196/141,-139/100) -> (85/36,196/83) Hyperbolic Matrix(2297,3192,444,617) (-82/59,-25/18) -> (31/6,26/5) Hyperbolic Matrix(727,1008,282,391) (-25/18,-18/13) -> (18/7,31/12) Hyperbolic Matrix(9071,12544,2510,3471) (-65/47,-112/81) -> (112/31,47/13) Hyperbolic Matrix(9073,12544,2512,3473) (-112/81,-47/34) -> (65/18,112/31) Hyperbolic Matrix(1175,1624,526,727) (-47/34,-29/21) -> (29/13,9/4) Hyperbolic Matrix(1177,1624,366,505) (-29/21,-40/29) -> (16/5,29/9) Hyperbolic Matrix(2295,3136,614,839) (-41/30,-56/41) -> (56/15,15/4) Hyperbolic Matrix(2297,3136,616,841) (-56/41,-15/11) -> (41/11,56/15) Hyperbolic Matrix(391,532,-330,-449) (-15/11,-19/14) -> (-19/16,-13/11) Hyperbolic Matrix(167,224,-126,-169) (-27/20,-4/3) -> (-4/3,-29/22) Parabolic Matrix(2913,3836,1234,1625) (-29/22,-25/19) -> (59/25,85/36) Hyperbolic Matrix(1343,1764,-1024,-1345) (-25/19,-21/16) -> (-21/16,-59/45) Parabolic Matrix(279,364,128,167) (-17/13,-13/10) -> (13/6,11/5) Hyperbolic Matrix(281,364,44,57) (-13/10,-22/17) -> (6/1,13/2) Hyperbolic Matrix(6607,8540,2772,3583) (-53/41,-84/65) -> (112/47,31/13) Hyperbolic Matrix(7953,10276,3338,4313) (-84/65,-31/24) -> (81/34,112/47) Hyperbolic Matrix(2407,3080,1706,2183) (-32/25,-55/43) -> (55/39,24/17) Hyperbolic Matrix(1511,1932,262,335) (-55/43,-23/18) -> (23/4,29/5) Hyperbolic Matrix(505,644,396,505) (-23/18,-14/11) -> (14/11,23/18) Hyperbolic Matrix(111,140,88,111) (-14/11,-5/4) -> (5/4,14/11) Hyperbolic Matrix(113,140,46,57) (-5/4,-11/9) -> (17/7,5/2) Hyperbolic Matrix(505,616,414,505) (-11/9,-28/23) -> (28/23,11/9) Hyperbolic Matrix(783,952,644,783) (-28/23,-17/14) -> (17/14,28/23) Hyperbolic Matrix(393,476,232,281) (-17/14,-6/5) -> (22/13,17/10) Hyperbolic Matrix(895,1064,376,447) (-6/5,-19/16) -> (19/8,50/21) Hyperbolic Matrix(167,196,-144,-169) (-13/11,-7/6) -> (-7/6,-15/13) Parabolic Matrix(559,644,388,447) (-15/13,-8/7) -> (36/25,13/9) Hyperbolic Matrix(279,308,202,223) (-9/8,-1/1) -> (29/21,47/34) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(223,-252,100,-113) (1/1,8/7) -> (20/9,29/13) Hyperbolic Matrix(169,-196,144,-167) (8/7,7/6) -> (7/6,20/17) Parabolic Matrix(449,-532,330,-391) (13/11,6/5) -> (34/25,15/11) Hyperbolic Matrix(503,-644,132,-169) (23/18,9/7) -> (19/5,23/6) Hyperbolic Matrix(391,-504,218,-281) (9/7,22/17) -> (34/19,9/5) Hyperbolic Matrix(449,-588,42,-55) (17/13,38/29) -> (10/1,11/1) Hyperbolic Matrix(2521,-3304,982,-1287) (38/29,21/16) -> (77/30,18/7) Hyperbolic Matrix(2407,-3164,938,-1233) (21/16,25/19) -> (59/23,77/30) Hyperbolic Matrix(615,-812,128,-169) (25/19,4/3) -> (24/5,53/11) Hyperbolic Matrix(393,-532,82,-111) (4/3,19/14) -> (19/4,24/5) Hyperbolic Matrix(225,-308,122,-167) (15/11,11/8) -> (11/6,13/7) Hyperbolic Matrix(447,-616,82,-113) (11/8,29/21) -> (27/5,11/2) Hyperbolic Matrix(1457,-2016,404,-559) (47/34,18/13) -> (18/5,65/18) Hyperbolic Matrix(281,-392,200,-279) (25/18,7/5) -> (7/5,31/22) Parabolic Matrix(7785,-10976,3296,-4647) (86/61,55/39) -> (111/47,26/11) Hyperbolic Matrix(1063,-1512,670,-953) (27/19,10/7) -> (46/29,27/17) Hyperbolic Matrix(895,-1288,312,-449) (23/16,36/25) -> (20/7,23/8) Hyperbolic Matrix(559,-812,232,-337) (13/9,16/11) -> (12/5,41/17) Hyperbolic Matrix(615,-896,116,-169) (16/11,19/13) -> (37/7,16/3) Hyperbolic Matrix(727,-1064,192,-281) (19/13,3/2) -> (53/14,19/5) Hyperbolic Matrix(393,-616,178,-279) (25/16,11/7) -> (11/5,31/14) Hyperbolic Matrix(503,-812,70,-113) (50/31,21/13) -> (7/1,22/3) Hyperbolic Matrix(225,-364,34,-55) (21/13,13/8) -> (13/2,7/1) Hyperbolic Matrix(167,-280,34,-57) (5/3,27/16) -> (29/6,5/1) Hyperbolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(895,-1596,346,-617) (16/9,25/14) -> (31/12,44/17) Hyperbolic Matrix(2239,-4004,940,-1681) (25/14,34/19) -> (50/21,81/34) Hyperbolic Matrix(223,-420,60,-113) (13/7,2/1) -> (26/7,41/11) Hyperbolic Matrix(783,-1736,152,-337) (31/14,51/23) -> (5/1,31/6) Hyperbolic Matrix(223,-504,50,-113) (9/4,25/11) -> (31/7,9/2) Hyperbolic Matrix(1513,-3444,590,-1343) (25/11,41/18) -> (41/16,59/23) Hyperbolic Matrix(281,-644,24,-55) (55/24,39/17) -> (11/1,1/0) Hyperbolic Matrix(169,-392,72,-167) (23/10,7/3) -> (7/3,33/14) Parabolic Matrix(1567,-3780,604,-1457) (41/17,70/29) -> (70/27,13/5) Hyperbolic Matrix(503,-1288,66,-169) (23/9,41/16) -> (15/2,23/3) Hyperbolic Matrix(673,-1764,256,-671) (34/13,21/8) -> (21/8,50/19) Parabolic Matrix(617,-1624,106,-279) (50/19,29/11) -> (29/5,6/1) Hyperbolic Matrix(673,-1820,186,-503) (27/10,19/7) -> (47/13,29/8) Hyperbolic Matrix(167,-476,20,-57) (17/6,20/7) -> (8/1,17/2) Hyperbolic Matrix(57,-196,16,-55) (10/3,7/2) -> (7/2,18/5) Parabolic Matrix(223,-840,30,-113) (15/4,34/9) -> (22/3,15/2) Hyperbolic Matrix(897,-3836,170,-727) (47/11,30/7) -> (58/11,37/7) Hyperbolic Matrix(337,-1764,64,-335) (26/5,21/4) -> (21/4,58/11) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(55,588,-42,-449) -> Matrix(1,0,-4,1) Matrix(111,1064,70,671) -> Matrix(1,0,16,1) Matrix(57,476,-20,-167) -> Matrix(3,-2,-4,3) Matrix(169,1288,-66,-503) -> Matrix(1,0,-4,1) Matrix(113,812,-70,-503) -> Matrix(1,-2,-4,9) Matrix(55,364,-34,-225) -> Matrix(1,0,-4,1) Matrix(225,1316,-86,-503) -> Matrix(3,2,-8,-5) Matrix(225,1288,98,561) -> Matrix(5,2,12,5) Matrix(169,952,30,169) -> Matrix(1,0,8,1) Matrix(111,616,20,111) -> Matrix(1,0,-4,1) Matrix(113,616,-82,-447) -> Matrix(1,0,-8,1) Matrix(169,896,-116,-615) -> Matrix(3,-2,-16,11) Matrix(391,2044,-268,-1401) -> Matrix(3,10,-16,-53) Matrix(391,2016,-250,-1289) -> Matrix(1,2,-4,-7) Matrix(111,532,-82,-393) -> Matrix(1,0,-4,1) Matrix(113,532,24,113) -> Matrix(1,0,0,1) Matrix(55,252,12,55) -> Matrix(1,2,0,1) Matrix(113,504,-50,-223) -> Matrix(3,2,-8,-5) Matrix(167,728,64,279) -> Matrix(1,0,4,1) Matrix(111,476,52,223) -> Matrix(5,4,16,13) Matrix(727,3108,-498,-2129) -> Matrix(25,18,-132,-95) Matrix(223,952,26,111) -> Matrix(3,2,-8,-5) Matrix(113,476,80,337) -> Matrix(7,4,40,23) Matrix(169,644,-132,-503) -> Matrix(13,6,-76,-35) Matrix(281,1064,-192,-727) -> Matrix(17,6,-88,-31) Matrix(839,3164,-520,-1961) -> Matrix(7,2,-32,-9) Matrix(391,1456,-286,-1065) -> Matrix(1,0,-8,1) Matrix(167,616,106,391) -> Matrix(1,0,4,1) Matrix(55,196,-16,-57) -> Matrix(3,2,-8,-5) Matrix(281,952,116,393) -> Matrix(5,2,12,5) Matrix(449,1512,-166,-559) -> Matrix(11,4,-36,-13) Matrix(111,364,68,223) -> Matrix(1,0,8,1) Matrix(337,1092,104,337) -> Matrix(7,2,24,7) Matrix(1007,3248,590,1903) -> Matrix(17,4,72,17) Matrix(279,896,52,167) -> Matrix(1,0,4,1) Matrix(167,532,70,223) -> Matrix(1,0,8,1) Matrix(449,1288,-312,-895) -> Matrix(1,0,-4,1) Matrix(503,1428,118,335) -> Matrix(7,4,12,7) Matrix(169,476,60,169) -> Matrix(11,6,20,11) Matrix(111,308,40,111) -> Matrix(9,4,20,9) Matrix(113,308,62,169) -> Matrix(5,2,12,5) Matrix(1231,3332,-890,-2409) -> Matrix(25,8,-172,-55) Matrix(167,448,104,279) -> Matrix(1,0,8,1) Matrix(169,448,106,281) -> Matrix(1,0,8,1) Matrix(671,1764,-256,-673) -> Matrix(3,2,-8,-5) Matrix(1401,3668,364,953) -> Matrix(1,0,4,1) Matrix(279,728,64,167) -> Matrix(1,0,4,1) Matrix(671,1736,-390,-1009) -> Matrix(7,2,-32,-9) Matrix(391,1008,282,727) -> Matrix(5,2,32,13) Matrix(1343,3444,-590,-1513) -> Matrix(13,4,-36,-11) Matrix(1455,3724,656,1679) -> Matrix(7,2,24,7) Matrix(505,1288,198,505) -> Matrix(1,0,8,1) Matrix(111,280,44,111) -> Matrix(1,0,4,1) Matrix(57,140,46,113) -> Matrix(5,2,32,13) Matrix(335,812,92,223) -> Matrix(1,0,4,1) Matrix(337,812,-232,-559) -> Matrix(5,2,-28,-11) Matrix(223,532,70,167) -> Matrix(1,0,8,1) Matrix(1399,3332,-1082,-2577) -> Matrix(3,-2,-16,11) Matrix(671,1596,494,1175) -> Matrix(1,0,8,1) Matrix(449,1064,284,673) -> Matrix(1,0,4,1) Matrix(167,392,-72,-169) -> Matrix(3,2,-8,-5) Matrix(4759,10976,-3424,-7897) -> Matrix(39,14,-248,-89) Matrix(2575,5936,534,1231) -> Matrix(1,0,4,1) Matrix(559,1288,194,447) -> Matrix(1,0,4,1) Matrix(561,1288,98,225) -> Matrix(5,2,12,5) Matrix(1343,3080,-1026,-2353) -> Matrix(5,2,-28,-11) Matrix(1455,3332,562,1287) -> Matrix(5,2,12,5) Matrix(503,1148,294,671) -> Matrix(11,4,52,19) Matrix(2129,4844,-1624,-3695) -> Matrix(11,4,-80,-29) Matrix(2071,4704,468,1063) -> Matrix(35,12,32,11) Matrix(4145,9408,938,2129) -> Matrix(61,20,64,21) Matrix(1679,3808,444,1007) -> Matrix(7,2,24,7) Matrix(113,252,-100,-223) -> Matrix(13,4,-88,-27) Matrix(279,616,-178,-393) -> Matrix(1,0,0,1) Matrix(167,364,128,279) -> Matrix(1,0,8,1) Matrix(337,728,156,337) -> Matrix(17,6,48,17) Matrix(391,840,182,391) -> Matrix(31,10,96,31) Matrix(223,476,52,111) -> Matrix(13,4,16,5) Matrix(167,308,-122,-225) -> Matrix(1,0,-4,1) Matrix(169,308,62,113) -> Matrix(5,2,12,5) Matrix(111,196,-64,-113) -> Matrix(15,4,-64,-17) Matrix(503,868,-390,-673) -> Matrix(53,12,-296,-67) Matrix(1791,3080,-1238,-2129) -> Matrix(19,4,-100,-21) Matrix(897,1540,392,673) -> Matrix(19,4,52,11) Matrix(671,1148,294,503) -> Matrix(19,4,52,11) Matrix(3361,5740,1968,3361) -> Matrix(1,0,8,1) Matrix(1903,3248,590,1007) -> Matrix(17,4,72,17) Matrix(559,952,394,671) -> Matrix(37,8,208,45) Matrix(281,476,232,393) -> Matrix(1,0,12,1) Matrix(1177,1988,730,1233) -> Matrix(9,2,40,9) Matrix(449,756,-332,-559) -> Matrix(1,0,0,1) Matrix(169,280,102,169) -> Matrix(9,2,40,9) Matrix(783,1288,476,783) -> Matrix(11,2,60,11) Matrix(393,644,274,449) -> Matrix(11,2,60,11) Matrix(223,364,68,111) -> Matrix(1,0,8,1) Matrix(449,728,346,561) -> Matrix(11,2,60,11) Matrix(1233,1988,730,1177) -> Matrix(9,2,40,9) Matrix(279,448,104,167) -> Matrix(1,0,8,1) Matrix(281,448,106,169) -> Matrix(1,0,8,1) Matrix(953,1512,-670,-1063) -> Matrix(21,2,-116,-11) Matrix(673,1064,284,449) -> Matrix(1,0,4,1) Matrix(391,616,106,167) -> Matrix(1,0,4,1) Matrix(841,1316,108,169) -> Matrix(7,2,-4,-1) Matrix(3081,4816,2186,3417) -> Matrix(33,10,188,57) Matrix(449,700,288,449) -> Matrix(15,4,56,15) Matrix(55,84,36,55) -> Matrix(9,2,40,9) Matrix(839,1232,190,279) -> Matrix(51,10,56,11) Matrix(2241,3248,928,1345) -> Matrix(21,4,68,13) Matrix(4313,6244,1664,2409) -> Matrix(11,2,60,11) Matrix(505,728,428,617) -> Matrix(11,2,60,11) Matrix(2297,3304,974,1401) -> Matrix(11,2,16,3) Matrix(449,644,274,393) -> Matrix(11,2,60,11) Matrix(393,560,40,57) -> Matrix(11,2,60,11) Matrix(6607,9408,4168,5935) -> Matrix(11,2,412,75) Matrix(3305,4704,2086,2969) -> Matrix(11,2,-116,-21) Matrix(671,952,394,559) -> Matrix(45,8,208,37) Matrix(337,476,80,113) -> Matrix(23,4,40,7) Matrix(279,392,-200,-281) -> Matrix(35,6,-216,-37) Matrix(785,1092,202,281) -> Matrix(13,2,32,5) Matrix(23687,32928,10030,13943) -> Matrix(139,22,120,19) Matrix(31585,43904,13376,18593) -> Matrix(165,26,184,29) Matrix(2297,3192,444,617) -> Matrix(13,2,32,5) Matrix(727,1008,282,391) -> Matrix(13,2,32,5) Matrix(9071,12544,2510,3471) -> Matrix(167,24,160,23) Matrix(9073,12544,2512,3473) -> Matrix(169,24,176,25) Matrix(1175,1624,526,727) -> Matrix(43,6,136,19) Matrix(1177,1624,366,505) -> Matrix(1,0,12,1) Matrix(2295,3136,614,839) -> Matrix(1,0,16,1) Matrix(2297,3136,616,841) -> Matrix(1,0,0,1) Matrix(391,532,-330,-449) -> Matrix(1,0,0,1) Matrix(167,224,-126,-169) -> Matrix(1,0,0,1) Matrix(2913,3836,1234,1625) -> Matrix(11,2,16,3) Matrix(1343,1764,-1024,-1345) -> Matrix(11,2,-72,-13) Matrix(279,364,128,167) -> Matrix(1,0,8,1) Matrix(281,364,44,57) -> Matrix(11,2,16,3) Matrix(6607,8540,2772,3583) -> Matrix(11,2,192,35) Matrix(7953,10276,3338,4313) -> Matrix(11,2,-160,-29) Matrix(2407,3080,1706,2183) -> Matrix(59,10,348,59) Matrix(1511,1932,262,335) -> Matrix(47,8,88,15) Matrix(505,644,396,505) -> Matrix(107,18,636,107) Matrix(111,140,88,111) -> Matrix(25,4,156,25) Matrix(113,140,46,57) -> Matrix(13,2,32,5) Matrix(505,616,414,505) -> Matrix(41,6,280,41) Matrix(783,952,644,783) -> Matrix(43,6,308,43) Matrix(393,476,232,281) -> Matrix(1,0,12,1) Matrix(895,1064,376,447) -> Matrix(1,0,8,1) Matrix(167,196,-144,-169) -> Matrix(11,2,-72,-13) Matrix(559,644,388,447) -> Matrix(1,0,12,1) Matrix(279,308,202,223) -> Matrix(15,2,112,15) Matrix(1,0,2,1) -> Matrix(1,0,16,1) Matrix(223,-252,100,-113) -> Matrix(27,-4,88,-13) Matrix(169,-196,144,-167) -> Matrix(13,-2,72,-11) Matrix(449,-532,330,-391) -> Matrix(1,0,0,1) Matrix(503,-644,132,-169) -> Matrix(35,-6,76,-13) Matrix(391,-504,218,-281) -> Matrix(45,-8,152,-27) Matrix(449,-588,42,-55) -> Matrix(1,0,-4,1) Matrix(2521,-3304,982,-1287) -> Matrix(1,0,-4,1) Matrix(2407,-3164,938,-1233) -> Matrix(11,-2,28,-5) Matrix(615,-812,128,-169) -> Matrix(1,0,-4,1) Matrix(393,-532,82,-111) -> Matrix(1,0,-4,1) Matrix(225,-308,122,-167) -> Matrix(1,0,-4,1) Matrix(447,-616,82,-113) -> Matrix(1,0,-8,1) Matrix(1457,-2016,404,-559) -> Matrix(41,-6,48,-7) Matrix(281,-392,200,-279) -> Matrix(37,-6,216,-35) Matrix(7785,-10976,3296,-4647) -> Matrix(57,-10,40,-7) Matrix(1063,-1512,670,-953) -> Matrix(11,-2,116,-21) Matrix(895,-1288,312,-449) -> Matrix(1,0,-4,1) Matrix(559,-812,232,-337) -> Matrix(11,-2,28,-5) Matrix(615,-896,116,-169) -> Matrix(11,-2,-16,3) Matrix(727,-1064,192,-281) -> Matrix(31,-6,88,-17) Matrix(393,-616,178,-279) -> Matrix(1,0,0,1) Matrix(503,-812,70,-113) -> Matrix(9,-2,-4,1) Matrix(225,-364,34,-55) -> Matrix(1,0,-4,1) Matrix(167,-280,34,-57) -> Matrix(1,0,-4,1) Matrix(113,-196,64,-111) -> Matrix(17,-4,64,-15) Matrix(895,-1596,346,-617) -> Matrix(7,-2,32,-9) Matrix(2239,-4004,940,-1681) -> Matrix(7,-2,-24,7) Matrix(223,-420,60,-113) -> Matrix(1,0,-4,1) Matrix(783,-1736,152,-337) -> Matrix(7,-2,4,-1) Matrix(223,-504,50,-113) -> Matrix(5,-2,8,-3) Matrix(1513,-3444,590,-1343) -> Matrix(11,-4,36,-13) Matrix(281,-644,24,-55) -> Matrix(5,-2,8,-3) Matrix(169,-392,72,-167) -> Matrix(5,-2,8,-3) Matrix(1567,-3780,604,-1457) -> Matrix(1,0,0,1) Matrix(503,-1288,66,-169) -> Matrix(1,0,-4,1) Matrix(673,-1764,256,-671) -> Matrix(5,-2,8,-3) Matrix(617,-1624,106,-279) -> Matrix(1,0,0,1) Matrix(673,-1820,186,-503) -> Matrix(7,-2,4,-1) Matrix(167,-476,20,-57) -> Matrix(3,-2,-4,3) Matrix(57,-196,16,-55) -> Matrix(5,-2,8,-3) Matrix(223,-840,30,-113) -> Matrix(1,0,-4,1) Matrix(897,-3836,170,-727) -> Matrix(11,-8,-4,3) Matrix(337,-1764,64,-335) -> Matrix(1,-4,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 32 Degree of the the map X: 64 Degree of the the map Y: 192 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 576 Minimal number of generators: 97 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 48 Genus: 25 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -7/1 -6/1 -4/1 -7/2 -10/3 -12/5 -7/3 -2/1 -7/4 -42/29 -7/5 -7/6 0/1 1/1 7/6 14/11 7/5 3/2 14/9 7/4 9/5 2/1 7/3 12/5 5/2 28/11 8/3 14/5 3/1 42/13 10/3 7/2 112/31 11/3 56/15 4/1 13/3 84/19 9/2 14/3 5/1 11/2 28/5 6/1 13/2 7/1 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 1/0 -6/1 1/0 -11/2 0/1 1/2 -5/1 1/0 -14/3 1/0 -9/2 -1/1 1/0 -22/5 -3/4 -13/3 1/0 -4/1 -1/2 1/0 -15/4 -1/4 0/1 -11/3 1/0 -7/2 -1/2 -17/5 -3/8 -27/8 -3/8 -1/3 -10/3 -1/4 -13/4 -1/3 -1/4 -16/5 -1/4 -1/6 -3/1 1/0 -14/5 -1/2 -11/4 -1/2 -2/5 -19/7 -7/20 -46/17 -5/16 -27/10 -1/3 -1/4 -8/3 -1/2 -1/4 -21/8 -1/2 -13/5 -1/4 -18/7 -1/4 -5/2 -1/2 0/1 -17/7 -1/4 -29/12 -1/3 -1/4 -12/5 -1/2 -1/4 -7/3 -1/2 -16/7 -1/2 -3/8 -25/11 -7/20 -34/15 -1/4 -9/4 -3/8 -1/3 -11/5 -1/4 -13/6 -3/8 -1/3 -2/1 -1/4 -11/6 -1/2 0/1 -9/5 -5/16 -7/4 -1/4 -19/11 -11/48 -31/18 -2/9 -7/32 -12/7 -1/4 -3/14 -41/24 -1/4 0/1 -70/41 -1/4 -29/17 -1/4 -17/10 -3/14 -1/5 -5/3 -1/4 -28/17 -1/5 -23/14 -1/5 -1/6 -18/11 -1/4 -13/8 -1/4 -1/5 -34/21 -1/4 -21/13 -1/4 -29/18 -1/4 -1/5 -8/5 -1/4 -1/6 -27/17 -1/8 -19/12 0/1 1/0 -11/7 -1/4 -14/9 -1/4 -3/2 -1/4 -1/5 -16/11 -3/16 -1/6 -29/20 -1/5 -3/16 -42/29 -3/16 -13/9 -3/16 -10/7 -3/16 -7/5 -1/6 -18/13 -3/20 -65/47 -15/104 -112/81 -1/7 -47/34 -1/7 -9/64 -29/21 -1/8 -11/8 -1/6 0/1 -26/19 -1/8 -41/30 -1/12 0/1 -56/41 0/1 -15/11 -1/4 -4/3 -1/4 -1/6 -13/10 -1/5 -3/16 -22/17 -3/16 -53/41 -19/104 -84/65 -2/11 -31/24 -2/11 -13/72 -9/7 -7/40 -14/11 -1/6 -5/4 -1/6 -2/13 -11/9 -3/20 -28/23 -1/7 -17/14 -1/7 -3/22 -6/5 -1/8 -13/11 -1/4 -7/6 -1/6 -8/7 -1/6 -3/20 -1/1 -1/8 0/1 0/1 1/1 1/8 7/6 1/6 6/5 1/8 11/9 3/20 5/4 2/13 1/6 14/11 1/6 9/7 7/40 22/17 3/16 13/10 3/16 1/5 4/3 1/6 1/4 15/11 1/4 11/8 0/1 1/6 7/5 1/6 17/12 1/6 3/17 27/19 5/28 10/7 3/16 13/9 3/16 16/11 1/6 3/16 3/2 1/5 1/4 14/9 1/4 11/7 1/4 19/12 0/1 1/0 46/29 1/12 27/17 1/8 8/5 1/6 1/4 21/13 1/4 13/8 1/5 1/4 18/11 1/4 5/3 1/4 17/10 1/5 3/14 29/17 1/4 12/7 3/14 1/4 7/4 1/4 16/9 1/4 5/18 25/14 9/32 2/7 34/19 7/24 9/5 5/16 11/6 0/1 1/2 13/7 1/0 2/1 1/4 11/5 1/4 9/4 1/3 3/8 7/3 1/2 19/8 0/1 1/4 31/13 1/8 12/5 1/4 1/2 41/17 1/4 70/29 1/4 29/12 1/4 1/3 17/7 1/4 5/2 0/1 1/2 28/11 0/1 23/9 1/4 18/7 1/4 13/5 1/4 34/13 3/8 21/8 1/2 29/11 1/0 8/3 1/4 1/2 27/10 1/4 1/3 19/7 7/20 11/4 2/5 1/2 14/5 1/2 3/1 1/0 16/5 1/6 1/4 29/9 1/4 42/13 1/4 13/4 1/4 1/3 10/3 1/4 7/2 1/2 18/5 3/4 65/18 15/16 1/1 112/31 1/1 47/13 9/8 29/8 1/1 1/0 11/3 1/0 26/7 1/0 41/11 -1/4 56/15 0/1 15/4 0/1 1/4 4/1 1/2 1/0 13/3 1/0 22/5 3/4 53/12 11/12 1/1 84/19 1/1 31/7 5/4 9/2 1/1 1/0 14/3 1/0 5/1 1/0 11/2 -1/2 0/1 28/5 0/1 17/3 1/4 6/1 1/0 13/2 1/1 1/0 7/1 1/0 8/1 -1/2 1/0 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(29,224,-18,-139) (-7/1,1/0) -> (-21/13,-29/18) Hyperbolic Matrix(55,364,-34,-225) (-7/1,-6/1) -> (-34/21,-21/13) Hyperbolic Matrix(29,168,-24,-139) (-6/1,-11/2) -> (-17/14,-6/5) Hyperbolic Matrix(27,140,16,83) (-11/2,-5/1) -> (5/3,17/10) Hyperbolic Matrix(29,140,6,29) (-5/1,-14/3) -> (14/3,5/1) Hyperbolic Matrix(55,252,12,55) (-14/3,-9/2) -> (9/2,14/3) Hyperbolic Matrix(113,504,-50,-223) (-9/2,-22/5) -> (-34/15,-9/4) Hyperbolic Matrix(167,728,64,279) (-22/5,-13/3) -> (13/5,34/13) Hyperbolic Matrix(27,112,20,83) (-13/3,-4/1) -> (4/3,15/11) Hyperbolic Matrix(29,112,22,85) (-4/1,-15/4) -> (13/10,4/3) Hyperbolic Matrix(83,308,-38,-141) (-15/4,-11/3) -> (-11/5,-13/6) Hyperbolic Matrix(55,196,-16,-57) (-11/3,-7/2) -> (-7/2,-17/5) Parabolic Matrix(281,952,116,393) (-17/5,-27/8) -> (29/12,17/7) Hyperbolic Matrix(449,1512,-166,-559) (-27/8,-10/3) -> (-46/17,-27/10) Hyperbolic Matrix(111,364,68,223) (-10/3,-13/4) -> (13/8,18/11) Hyperbolic Matrix(253,812,-148,-475) (-13/4,-16/5) -> (-12/7,-41/24) Hyperbolic Matrix(167,532,70,223) (-16/5,-3/1) -> (31/13,12/5) Hyperbolic Matrix(29,84,10,29) (-3/1,-14/5) -> (14/5,3/1) Hyperbolic Matrix(111,308,40,111) (-14/5,-11/4) -> (11/4,14/5) Hyperbolic Matrix(113,308,62,169) (-11/4,-19/7) -> (9/5,11/6) Hyperbolic Matrix(1231,3332,-890,-2409) (-19/7,-46/17) -> (-18/13,-65/47) Hyperbolic Matrix(83,224,10,27) (-27/10,-8/3) -> (8/1,1/0) Hyperbolic Matrix(85,224,-74,-195) (-8/3,-21/8) -> (-7/6,-8/7) Hyperbolic Matrix(139,364,-118,-309) (-21/8,-13/5) -> (-13/11,-7/6) Hyperbolic Matrix(141,364,98,253) (-13/5,-18/7) -> (10/7,13/9) Hyperbolic Matrix(197,504,-120,-307) (-18/7,-5/2) -> (-23/14,-18/11) Hyperbolic Matrix(57,140,46,113) (-5/2,-17/7) -> (11/9,5/4) Hyperbolic Matrix(335,812,92,223) (-17/7,-29/12) -> (29/8,11/3) Hyperbolic Matrix(337,812,-232,-559) (-29/12,-12/5) -> (-16/11,-29/20) Hyperbolic Matrix(83,196,-36,-85) (-12/5,-7/3) -> (-7/3,-16/7) Parabolic Matrix(197,448,62,141) (-16/7,-25/11) -> (3/1,16/5) Hyperbolic Matrix(1037,2352,-802,-1819) (-25/11,-34/15) -> (-22/17,-53/41) Hyperbolic Matrix(139,308,88,195) (-9/4,-11/5) -> (11/7,19/12) Hyperbolic Matrix(197,420,-144,-307) (-13/6,-2/1) -> (-26/19,-41/30) Hyperbolic Matrix(167,308,-122,-225) (-2/1,-11/6) -> (-11/8,-26/19) Hyperbolic Matrix(169,308,62,113) (-11/6,-9/5) -> (19/7,11/4) Hyperbolic Matrix(111,196,-64,-113) (-9/5,-7/4) -> (-7/4,-19/11) Parabolic Matrix(503,868,-390,-673) (-19/11,-31/18) -> (-31/24,-9/7) Hyperbolic Matrix(309,532,212,365) (-31/18,-12/7) -> (16/11,3/2) Hyperbolic Matrix(1541,2632,476,813) (-41/24,-70/41) -> (42/13,13/4) Hyperbolic Matrix(1903,3248,590,1007) (-70/41,-29/17) -> (29/9,42/13) Hyperbolic Matrix(559,952,394,671) (-29/17,-17/10) -> (17/12,27/19) Hyperbolic Matrix(83,140,16,27) (-17/10,-5/3) -> (5/1,11/2) Hyperbolic Matrix(475,784,186,307) (-5/3,-28/17) -> (28/11,23/9) Hyperbolic Matrix(477,784,188,309) (-28/17,-23/14) -> (5/2,28/11) Hyperbolic Matrix(223,364,68,111) (-18/11,-13/8) -> (13/4,10/3) Hyperbolic Matrix(449,728,346,561) (-13/8,-34/21) -> (22/17,13/10) Hyperbolic Matrix(279,448,104,167) (-29/18,-8/5) -> (8/3,27/10) Hyperbolic Matrix(281,448,106,169) (-8/5,-27/17) -> (29/11,8/3) Hyperbolic Matrix(1147,1820,-830,-1317) (-27/17,-19/12) -> (-47/34,-29/21) Hyperbolic Matrix(195,308,88,139) (-19/12,-11/7) -> (11/5,9/4) Hyperbolic Matrix(197,308,126,197) (-11/7,-14/9) -> (14/9,11/7) Hyperbolic Matrix(55,84,36,55) (-14/9,-3/2) -> (3/2,14/9) Hyperbolic Matrix(307,448,172,251) (-3/2,-16/11) -> (16/9,25/14) Hyperbolic Matrix(2241,3248,928,1345) (-29/20,-42/29) -> (70/29,29/12) Hyperbolic Matrix(1819,2632,754,1091) (-42/29,-13/9) -> (41/17,70/29) Hyperbolic Matrix(253,364,98,141) (-13/9,-10/7) -> (18/7,13/5) Hyperbolic Matrix(139,196,-100,-141) (-10/7,-7/5) -> (-7/5,-18/13) Parabolic Matrix(9071,12544,2510,3471) (-65/47,-112/81) -> (112/31,47/13) Hyperbolic Matrix(9073,12544,2512,3473) (-112/81,-47/34) -> (65/18,112/31) Hyperbolic Matrix(589,812,346,477) (-29/21,-11/8) -> (17/10,29/17) Hyperbolic Matrix(2295,3136,614,839) (-41/30,-56/41) -> (56/15,15/4) Hyperbolic Matrix(2297,3136,616,841) (-56/41,-15/11) -> (41/11,56/15) Hyperbolic Matrix(83,112,20,27) (-15/11,-4/3) -> (4/1,13/3) Hyperbolic Matrix(85,112,22,29) (-4/3,-13/10) -> (15/4,4/1) Hyperbolic Matrix(281,364,44,57) (-13/10,-22/17) -> (6/1,13/2) Hyperbolic Matrix(5459,7056,1234,1595) (-53/41,-84/65) -> (84/19,31/7) Hyperbolic Matrix(5461,7056,1236,1597) (-84/65,-31/24) -> (53/12,84/19) Hyperbolic Matrix(197,252,154,197) (-9/7,-14/11) -> (14/11,9/7) Hyperbolic Matrix(111,140,88,111) (-14/11,-5/4) -> (5/4,14/11) Hyperbolic Matrix(113,140,46,57) (-5/4,-11/9) -> (17/7,5/2) Hyperbolic Matrix(643,784,114,139) (-11/9,-28/23) -> (28/5,17/3) Hyperbolic Matrix(645,784,116,141) (-28/23,-17/14) -> (11/2,28/5) Hyperbolic Matrix(307,364,70,83) (-6/5,-13/11) -> (13/3,22/5) Hyperbolic Matrix(197,224,124,141) (-8/7,-1/1) -> (27/17,8/5) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(195,-224,74,-85) (1/1,7/6) -> (21/8,29/11) Hyperbolic Matrix(309,-364,118,-139) (7/6,6/5) -> (34/13,21/8) Hyperbolic Matrix(139,-168,24,-29) (6/5,11/9) -> (17/3,6/1) Hyperbolic Matrix(391,-504,218,-281) (9/7,22/17) -> (34/19,9/5) Hyperbolic Matrix(225,-308,122,-167) (15/11,11/8) -> (11/6,13/7) Hyperbolic Matrix(141,-196,100,-139) (11/8,7/5) -> (7/5,17/12) Parabolic Matrix(1063,-1512,670,-953) (27/19,10/7) -> (46/29,27/17) Hyperbolic Matrix(559,-812,232,-337) (13/9,16/11) -> (12/5,41/17) Hyperbolic Matrix(2101,-3332,582,-923) (19/12,46/29) -> (18/5,65/18) Hyperbolic Matrix(139,-224,18,-29) (8/5,21/13) -> (7/1,8/1) Hyperbolic Matrix(225,-364,34,-55) (21/13,13/8) -> (13/2,7/1) Hyperbolic Matrix(307,-504,120,-197) (18/11,5/3) -> (23/9,18/7) Hyperbolic Matrix(475,-812,148,-253) (29/17,12/7) -> (16/5,29/9) Hyperbolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(1315,-2352,298,-533) (25/14,34/19) -> (22/5,53/12) Hyperbolic Matrix(223,-420,60,-113) (13/7,2/1) -> (26/7,41/11) Hyperbolic Matrix(141,-308,38,-83) (2/1,11/5) -> (11/3,26/7) Hyperbolic Matrix(85,-196,36,-83) (9/4,7/3) -> (7/3,19/8) Parabolic Matrix(365,-868,82,-195) (19/8,31/13) -> (31/7,9/2) Hyperbolic Matrix(673,-1820,186,-503) (27/10,19/7) -> (47/13,29/8) Hyperbolic Matrix(57,-196,16,-55) (10/3,7/2) -> (7/2,18/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(29,224,-18,-139) -> Matrix(1,-1,-4,5) Matrix(55,364,-34,-225) -> Matrix(1,0,-4,1) Matrix(29,168,-24,-139) -> Matrix(1,1,-8,-7) Matrix(27,140,16,83) -> Matrix(1,1,4,5) Matrix(29,140,6,29) -> Matrix(1,1,0,1) Matrix(55,252,12,55) -> Matrix(1,2,0,1) Matrix(113,504,-50,-223) -> Matrix(3,2,-8,-5) Matrix(167,728,64,279) -> Matrix(1,0,4,1) Matrix(27,112,20,83) -> Matrix(1,1,4,5) Matrix(29,112,22,85) -> Matrix(1,1,4,5) Matrix(83,308,-38,-141) -> Matrix(1,1,-4,-3) Matrix(55,196,-16,-57) -> Matrix(3,2,-8,-5) Matrix(281,952,116,393) -> Matrix(5,2,12,5) Matrix(449,1512,-166,-559) -> Matrix(11,4,-36,-13) Matrix(111,364,68,223) -> Matrix(1,0,8,1) Matrix(253,812,-148,-475) -> Matrix(3,1,-16,-5) Matrix(167,532,70,223) -> Matrix(1,0,8,1) Matrix(29,84,10,29) -> Matrix(1,1,0,1) Matrix(111,308,40,111) -> Matrix(9,4,20,9) Matrix(113,308,62,169) -> Matrix(5,2,12,5) Matrix(1231,3332,-890,-2409) -> Matrix(25,8,-172,-55) Matrix(83,224,10,27) -> Matrix(3,1,-4,-1) Matrix(85,224,-74,-195) -> Matrix(1,1,-8,-7) Matrix(139,364,-118,-309) -> Matrix(3,1,-16,-5) Matrix(141,364,98,253) -> Matrix(1,1,4,5) Matrix(197,504,-120,-307) -> Matrix(3,1,-16,-5) Matrix(57,140,46,113) -> Matrix(5,2,32,13) Matrix(335,812,92,223) -> Matrix(1,0,4,1) Matrix(337,812,-232,-559) -> Matrix(5,2,-28,-11) Matrix(83,196,-36,-85) -> Matrix(1,1,-4,-3) Matrix(197,448,62,141) -> Matrix(3,1,20,7) Matrix(1037,2352,-802,-1819) -> Matrix(17,5,-92,-27) Matrix(139,308,88,195) -> Matrix(3,1,8,3) Matrix(197,420,-144,-307) -> Matrix(3,1,-28,-9) Matrix(167,308,-122,-225) -> Matrix(1,0,-4,1) Matrix(169,308,62,113) -> Matrix(5,2,12,5) Matrix(111,196,-64,-113) -> Matrix(15,4,-64,-17) Matrix(503,868,-390,-673) -> Matrix(53,12,-296,-67) Matrix(309,532,212,365) -> Matrix(23,5,124,27) Matrix(1541,2632,476,813) -> Matrix(3,1,8,3) Matrix(1903,3248,590,1007) -> Matrix(17,4,72,17) Matrix(559,952,394,671) -> Matrix(37,8,208,45) Matrix(83,140,16,27) -> Matrix(5,1,4,1) Matrix(475,784,186,307) -> Matrix(5,1,24,5) Matrix(477,784,188,309) -> Matrix(5,1,4,1) Matrix(223,364,68,111) -> Matrix(1,0,8,1) Matrix(449,728,346,561) -> Matrix(11,2,60,11) Matrix(279,448,104,167) -> Matrix(1,0,8,1) Matrix(281,448,106,169) -> Matrix(1,0,8,1) Matrix(1147,1820,-830,-1317) -> Matrix(9,1,-64,-7) Matrix(195,308,88,139) -> Matrix(3,1,8,3) Matrix(197,308,126,197) -> Matrix(3,1,8,3) Matrix(55,84,36,55) -> Matrix(9,2,40,9) Matrix(307,448,172,251) -> Matrix(37,7,132,25) Matrix(2241,3248,928,1345) -> Matrix(21,4,68,13) Matrix(1819,2632,754,1091) -> Matrix(5,1,4,1) Matrix(253,364,98,141) -> Matrix(5,1,4,1) Matrix(139,196,-100,-141) -> Matrix(17,3,-108,-19) Matrix(9071,12544,2510,3471) -> Matrix(167,24,160,23) Matrix(9073,12544,2512,3473) -> Matrix(169,24,176,25) Matrix(589,812,346,477) -> Matrix(9,1,44,5) Matrix(2295,3136,614,839) -> Matrix(1,0,16,1) Matrix(2297,3136,616,841) -> Matrix(1,0,0,1) Matrix(83,112,20,27) -> Matrix(5,1,4,1) Matrix(85,112,22,29) -> Matrix(5,1,4,1) Matrix(281,364,44,57) -> Matrix(11,2,16,3) Matrix(5459,7056,1234,1595) -> Matrix(159,29,148,27) Matrix(5461,7056,1236,1597) -> Matrix(193,35,204,37) Matrix(197,252,154,197) -> Matrix(41,7,240,41) Matrix(111,140,88,111) -> Matrix(25,4,156,25) Matrix(113,140,46,57) -> Matrix(13,2,32,5) Matrix(643,784,114,139) -> Matrix(7,1,48,7) Matrix(645,784,116,141) -> Matrix(7,1,-36,-5) Matrix(307,364,70,83) -> Matrix(5,1,4,1) Matrix(197,224,124,141) -> Matrix(7,1,48,7) Matrix(1,0,2,1) -> Matrix(1,0,16,1) Matrix(195,-224,74,-85) -> Matrix(7,-1,8,-1) Matrix(309,-364,118,-139) -> Matrix(5,-1,16,-3) Matrix(139,-168,24,-29) -> Matrix(7,-1,8,-1) Matrix(391,-504,218,-281) -> Matrix(45,-8,152,-27) Matrix(225,-308,122,-167) -> Matrix(1,0,-4,1) Matrix(141,-196,100,-139) -> Matrix(19,-3,108,-17) Matrix(1063,-1512,670,-953) -> Matrix(11,-2,116,-21) Matrix(559,-812,232,-337) -> Matrix(11,-2,28,-5) Matrix(2101,-3332,582,-923) -> Matrix(15,-1,16,-1) Matrix(139,-224,18,-29) -> Matrix(5,-1,-4,1) Matrix(225,-364,34,-55) -> Matrix(1,0,-4,1) Matrix(307,-504,120,-197) -> Matrix(5,-1,16,-3) Matrix(475,-812,148,-253) -> Matrix(5,-1,16,-3) Matrix(113,-196,64,-111) -> Matrix(17,-4,64,-15) Matrix(1315,-2352,298,-533) -> Matrix(45,-13,52,-15) Matrix(223,-420,60,-113) -> Matrix(1,0,-4,1) Matrix(141,-308,38,-83) -> Matrix(3,-1,4,-1) Matrix(85,-196,36,-83) -> Matrix(3,-1,4,-1) Matrix(365,-868,82,-195) -> Matrix(3,-1,4,-1) Matrix(673,-1820,186,-503) -> Matrix(7,-2,4,-1) Matrix(57,-196,16,-55) -> Matrix(5,-2,8,-3) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 32 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 0/1 8 1 1/1 1/8 1 28 7/6 1/6 2 4 6/5 1/8 1 14 11/9 3/20 1 28 5/4 (2/13,1/6) 0 28 14/11 1/6 11 2 9/7 7/40 1 28 22/17 3/16 1 14 13/10 (3/16,1/5) 0 28 4/3 0 7 15/11 1/4 1 28 11/8 (0/1,1/6) 0 28 7/5 1/6 3 4 17/12 (1/6,3/17) 0 28 27/19 5/28 1 28 10/7 3/16 1 14 13/9 3/16 1 28 16/11 0 7 3/2 (1/5,1/4) 0 28 14/9 1/4 3 2 11/7 1/4 1 28 19/12 (0/1,1/0) 0 28 46/29 1/12 1 14 27/17 1/8 1 28 8/5 0 7 21/13 1/4 1 4 13/8 (1/5,1/4) 0 28 18/11 1/4 1 14 5/3 1/4 1 28 17/10 (1/5,3/14) 0 28 29/17 1/4 1 28 12/7 0 7 7/4 1/4 4 4 16/9 0 7 25/14 (9/32,2/7) 0 28 34/19 7/24 1 14 9/5 5/16 1 28 11/6 (0/1,1/2) 0 28 13/7 1/0 1 28 2/1 1/4 1 14 11/5 1/4 1 28 9/4 (1/3,3/8) 0 28 7/3 1/2 1 4 19/8 (0/1,1/4) 0 28 31/13 1/8 1 28 12/5 0 7 41/17 1/4 1 28 70/29 1/4 1 2 29/12 (1/4,1/3) 0 28 17/7 1/4 1 28 5/2 (0/1,1/2) 0 28 28/11 0/1 2 1 23/9 1/4 1 28 18/7 1/4 1 14 13/5 1/4 1 28 34/13 3/8 1 14 21/8 1/2 2 4 29/11 1/0 1 28 8/3 0 7 27/10 (1/4,1/3) 0 28 19/7 7/20 1 28 11/4 (2/5,1/2) 0 28 14/5 1/2 5 2 3/1 1/0 1 28 16/5 0 7 29/9 1/4 1 28 42/13 1/4 5 2 13/4 (1/4,1/3) 0 28 10/3 1/4 1 14 7/2 1/2 2 4 18/5 3/4 1 14 65/18 (15/16,1/1) 0 28 112/31 1/1 24 1 47/13 9/8 1 28 29/8 (1/1,1/0) 0 28 11/3 1/0 1 28 26/7 1/0 1 14 41/11 -1/4 1 28 56/15 0/1 8 1 15/4 (0/1,1/4) 0 28 4/1 0 7 13/3 1/0 1 28 22/5 3/4 1 14 53/12 (11/12,1/1) 0 28 84/19 1/1 16 1 31/7 5/4 1 28 9/2 (1/1,1/0) 0 28 14/3 1/0 1 2 5/1 1/0 1 28 11/2 (-1/2,0/1) 0 28 28/5 0/1 6 1 17/3 1/4 1 28 6/1 1/0 1 14 13/2 (1/1,1/0) 0 28 7/1 1/0 1 4 8/1 0 7 1/0 (0/1,1/0) 0 28 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(195,-224,74,-85) (1/1,7/6) -> (21/8,29/11) Hyperbolic Matrix(309,-364,118,-139) (7/6,6/5) -> (34/13,21/8) Hyperbolic Matrix(139,-168,24,-29) (6/5,11/9) -> (17/3,6/1) Hyperbolic Matrix(113,-140,46,-57) (11/9,5/4) -> (17/7,5/2) Glide Reflection Matrix(111,-140,88,-111) (5/4,14/11) -> (5/4,14/11) Reflection Matrix(197,-252,154,-197) (14/11,9/7) -> (14/11,9/7) Reflection Matrix(391,-504,218,-281) (9/7,22/17) -> (34/19,9/5) Hyperbolic Matrix(281,-364,44,-57) (22/17,13/10) -> (6/1,13/2) Glide Reflection Matrix(85,-112,22,-29) (13/10,4/3) -> (15/4,4/1) Glide Reflection Matrix(83,-112,20,-27) (4/3,15/11) -> (4/1,13/3) Glide Reflection Matrix(225,-308,122,-167) (15/11,11/8) -> (11/6,13/7) Hyperbolic Matrix(141,-196,100,-139) (11/8,7/5) -> (7/5,17/12) Parabolic Matrix(671,-952,394,-559) (17/12,27/19) -> (17/10,29/17) Glide Reflection Matrix(1063,-1512,670,-953) (27/19,10/7) -> (46/29,27/17) Hyperbolic Matrix(253,-364,98,-141) (10/7,13/9) -> (18/7,13/5) Glide Reflection Matrix(559,-812,232,-337) (13/9,16/11) -> (12/5,41/17) Hyperbolic Matrix(307,-448,172,-251) (16/11,3/2) -> (16/9,25/14) Glide Reflection Matrix(55,-84,36,-55) (3/2,14/9) -> (3/2,14/9) Reflection Matrix(197,-308,126,-197) (14/9,11/7) -> (14/9,11/7) Reflection Matrix(195,-308,88,-139) (11/7,19/12) -> (11/5,9/4) Glide Reflection Matrix(2101,-3332,582,-923) (19/12,46/29) -> (18/5,65/18) Hyperbolic Matrix(281,-448,106,-169) (27/17,8/5) -> (29/11,8/3) Glide Reflection Matrix(139,-224,18,-29) (8/5,21/13) -> (7/1,8/1) Hyperbolic Matrix(225,-364,34,-55) (21/13,13/8) -> (13/2,7/1) Hyperbolic Matrix(223,-364,68,-111) (13/8,18/11) -> (13/4,10/3) Glide Reflection Matrix(307,-504,120,-197) (18/11,5/3) -> (23/9,18/7) Hyperbolic Matrix(83,-140,16,-27) (5/3,17/10) -> (5/1,11/2) Glide Reflection Matrix(475,-812,148,-253) (29/17,12/7) -> (16/5,29/9) Hyperbolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(1315,-2352,298,-533) (25/14,34/19) -> (22/5,53/12) Hyperbolic Matrix(169,-308,62,-113) (9/5,11/6) -> (19/7,11/4) Glide Reflection Matrix(223,-420,60,-113) (13/7,2/1) -> (26/7,41/11) Hyperbolic Matrix(141,-308,38,-83) (2/1,11/5) -> (11/3,26/7) Hyperbolic Matrix(85,-196,36,-83) (9/4,7/3) -> (7/3,19/8) Parabolic Matrix(365,-868,82,-195) (19/8,31/13) -> (31/7,9/2) Hyperbolic Matrix(223,-532,70,-167) (31/13,12/5) -> (3/1,16/5) Glide Reflection Matrix(2379,-5740,986,-2379) (41/17,70/29) -> (41/17,70/29) Reflection Matrix(1681,-4060,696,-1681) (70/29,29/12) -> (70/29,29/12) Reflection Matrix(335,-812,92,-223) (29/12,17/7) -> (29/8,11/3) Glide Reflection Matrix(111,-280,44,-111) (5/2,28/11) -> (5/2,28/11) Reflection Matrix(505,-1288,198,-505) (28/11,23/9) -> (28/11,23/9) Reflection Matrix(279,-728,64,-167) (13/5,34/13) -> (13/3,22/5) Glide Reflection Matrix(83,-224,10,-27) (8/3,27/10) -> (8/1,1/0) Glide Reflection Matrix(673,-1820,186,-503) (27/10,19/7) -> (47/13,29/8) Hyperbolic Matrix(111,-308,40,-111) (11/4,14/5) -> (11/4,14/5) Reflection Matrix(29,-84,10,-29) (14/5,3/1) -> (14/5,3/1) Reflection Matrix(755,-2436,234,-755) (29/9,42/13) -> (29/9,42/13) Reflection Matrix(337,-1092,104,-337) (42/13,13/4) -> (42/13,13/4) Reflection Matrix(57,-196,16,-55) (10/3,7/2) -> (7/2,18/5) Parabolic Matrix(4031,-14560,1116,-4031) (65/18,112/31) -> (65/18,112/31) Reflection Matrix(2913,-10528,806,-2913) (112/31,47/13) -> (112/31,47/13) Reflection Matrix(1231,-4592,330,-1231) (41/11,56/15) -> (41/11,56/15) Reflection Matrix(449,-1680,120,-449) (56/15,15/4) -> (56/15,15/4) Reflection Matrix(2015,-8904,456,-2015) (53/12,84/19) -> (53/12,84/19) Reflection Matrix(1177,-5208,266,-1177) (84/19,31/7) -> (84/19,31/7) Reflection Matrix(55,-252,12,-55) (9/2,14/3) -> (9/2,14/3) Reflection Matrix(29,-140,6,-29) (14/3,5/1) -> (14/3,5/1) Reflection Matrix(111,-616,20,-111) (11/2,28/5) -> (11/2,28/5) Reflection Matrix(169,-952,30,-169) (28/5,17/3) -> (28/5,17/3) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,2,-1) -> Matrix(1,0,16,-1) (0/1,1/1) -> (0/1,1/8) Matrix(195,-224,74,-85) -> Matrix(7,-1,8,-1) Matrix(309,-364,118,-139) -> Matrix(5,-1,16,-3) 1/4 Matrix(139,-168,24,-29) -> Matrix(7,-1,8,-1) Matrix(113,-140,46,-57) -> Matrix(13,-2,32,-5) Matrix(111,-140,88,-111) -> Matrix(25,-4,156,-25) (5/4,14/11) -> (2/13,1/6) Matrix(197,-252,154,-197) -> Matrix(41,-7,240,-41) (14/11,9/7) -> (1/6,7/40) Matrix(391,-504,218,-281) -> Matrix(45,-8,152,-27) Matrix(281,-364,44,-57) -> Matrix(11,-2,16,-3) Matrix(85,-112,22,-29) -> Matrix(5,-1,4,-1) Matrix(83,-112,20,-27) -> Matrix(5,-1,4,-1) Matrix(225,-308,122,-167) -> Matrix(1,0,-4,1) 0/1 Matrix(141,-196,100,-139) -> Matrix(19,-3,108,-17) 1/6 Matrix(671,-952,394,-559) -> Matrix(45,-8,208,-37) Matrix(1063,-1512,670,-953) -> Matrix(11,-2,116,-21) Matrix(253,-364,98,-141) -> Matrix(5,-1,4,-1) Matrix(559,-812,232,-337) -> Matrix(11,-2,28,-5) Matrix(307,-448,172,-251) -> Matrix(37,-7,132,-25) Matrix(55,-84,36,-55) -> Matrix(9,-2,40,-9) (3/2,14/9) -> (1/5,1/4) Matrix(197,-308,126,-197) -> Matrix(3,-1,8,-3) (14/9,11/7) -> (1/4,1/2) Matrix(195,-308,88,-139) -> Matrix(3,-1,8,-3) *** -> (1/4,1/2) Matrix(2101,-3332,582,-923) -> Matrix(15,-1,16,-1) Matrix(281,-448,106,-169) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(139,-224,18,-29) -> Matrix(5,-1,-4,1) Matrix(225,-364,34,-55) -> Matrix(1,0,-4,1) 0/1 Matrix(223,-364,68,-111) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(307,-504,120,-197) -> Matrix(5,-1,16,-3) 1/4 Matrix(83,-140,16,-27) -> Matrix(5,-1,4,-1) Matrix(475,-812,148,-253) -> Matrix(5,-1,16,-3) 1/4 Matrix(113,-196,64,-111) -> Matrix(17,-4,64,-15) 1/4 Matrix(1315,-2352,298,-533) -> Matrix(45,-13,52,-15) Matrix(169,-308,62,-113) -> Matrix(5,-2,12,-5) *** -> (1/3,1/2) Matrix(223,-420,60,-113) -> Matrix(1,0,-4,1) 0/1 Matrix(141,-308,38,-83) -> Matrix(3,-1,4,-1) 1/2 Matrix(85,-196,36,-83) -> Matrix(3,-1,4,-1) 1/2 Matrix(365,-868,82,-195) -> Matrix(3,-1,4,-1) 1/2 Matrix(223,-532,70,-167) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(2379,-5740,986,-2379) -> Matrix(3,-1,8,-3) (41/17,70/29) -> (1/4,1/2) Matrix(1681,-4060,696,-1681) -> Matrix(7,-2,24,-7) (70/29,29/12) -> (1/4,1/3) Matrix(335,-812,92,-223) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(111,-280,44,-111) -> Matrix(1,0,4,-1) (5/2,28/11) -> (0/1,1/2) Matrix(505,-1288,198,-505) -> Matrix(1,0,8,-1) (28/11,23/9) -> (0/1,1/4) Matrix(279,-728,64,-167) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(83,-224,10,-27) -> Matrix(3,-1,-4,1) Matrix(673,-1820,186,-503) -> Matrix(7,-2,4,-1) Matrix(111,-308,40,-111) -> Matrix(9,-4,20,-9) (11/4,14/5) -> (2/5,1/2) Matrix(29,-84,10,-29) -> Matrix(-1,1,0,1) (14/5,3/1) -> (1/2,1/0) Matrix(755,-2436,234,-755) -> Matrix(13,-3,56,-13) (29/9,42/13) -> (3/14,1/4) Matrix(337,-1092,104,-337) -> Matrix(7,-2,24,-7) (42/13,13/4) -> (1/4,1/3) Matrix(57,-196,16,-55) -> Matrix(5,-2,8,-3) 1/2 Matrix(4031,-14560,1116,-4031) -> Matrix(31,-30,32,-31) (65/18,112/31) -> (15/16,1/1) Matrix(2913,-10528,806,-2913) -> Matrix(17,-18,16,-17) (112/31,47/13) -> (1/1,9/8) Matrix(1231,-4592,330,-1231) -> Matrix(-1,0,8,1) (41/11,56/15) -> (-1/4,0/1) Matrix(449,-1680,120,-449) -> Matrix(1,0,8,-1) (56/15,15/4) -> (0/1,1/4) Matrix(2015,-8904,456,-2015) -> Matrix(23,-22,24,-23) (53/12,84/19) -> (11/12,1/1) Matrix(1177,-5208,266,-1177) -> Matrix(9,-10,8,-9) (84/19,31/7) -> (1/1,5/4) Matrix(55,-252,12,-55) -> Matrix(-1,2,0,1) (9/2,14/3) -> (1/1,1/0) Matrix(29,-140,6,-29) -> Matrix(-1,1,0,1) (14/3,5/1) -> (1/2,1/0) Matrix(111,-616,20,-111) -> Matrix(-1,0,4,1) (11/2,28/5) -> (-1/2,0/1) Matrix(169,-952,30,-169) -> Matrix(1,0,8,-1) (28/5,17/3) -> (0/1,1/4) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.